Related papers: Computing an Integer Prime Factoring in O(n^2.5)
The article is taken out.
We present an efficient and elementary algorithm for computing the number of primes up to $N$ in $\tilde{O}(\sqrt N)$ time, improving upon the existing combinatorial methods that require $\tilde{O}(N ^ {2/3})$ time. Our method has a similar…
This paper has been withdrawn by the author(s), due a mistake of factor 1/2.
Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of a positive integer $N$ in $N^{2/9+o(1)}$ bit operations. Prior to this breakthrough, the best known complexity bound for this problem…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…
The paper is being withdrawn since the authors felt that the submission is a little premature after a careful reading by some of the experts in this field.
This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
This paper has been withdrawn
This paper has been withdrawn by the authors, due to a crucial error in beta functions.
The best deterministic unconditionally proven integer factorization algorithms have exponential running time complexities of O(N^(1/4)) arithmetic operations, and conditional on the Riemann hypothesis, there is a deterministic algorithm of…
The unit cost model is both convenient and largely realistic for describing integer decision algorithms over (+,*). Additional operations like division with remainder or bitwise conjunction, although equally supported by computing hardware,…
This paper had been withdrawn because the prime reported effect had not been confirmed in further investigations (see arXiv:0812.4488 [hep-lat]).
This paper is withdrawn. See quant-ph/9806031 for a discussion.
This article has been withdrawn.
The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.
This submission has been withdrawn by arXiv admins due to fraudulent affiliation claims by the original submitter.
An algorithm counting the number of ones in a binary word is presented running in time $O(\log\log b)$ where $b$ is the number of ones. The operations available include bit-wise logical operations and multiplication.
An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…